We describe the state of electrons inside specific orbitals:

We assign each orbital a number from 0,1,2...
In each orbital each electron has a specific energy level $E_0,E_1,E_2,...$ 
Electrons in a particular orbital x are in the corresponding quantum state $\ket{x}$

![[Pasted image 20260805145524.png]]
![[Pasted image 20260805145536.png]]

### Time evolution of a quantum state

![[Pasted image 20260805145615.png]]


### Energy / Hamiltonian

From now on we assume there are only finitely many orbitals N. (not really true)

The total energy of an Electron can be calculated as:
![[Pasted image 20260805150241.png]]
![[Pasted image 20260805150253.png]]

### Schrödingers equation

![[Pasted image 20260805151253.png]]![[Pasted image 20260805151259.png]]